Organizational Dynamics Over the BusinessCycle: A View on Jobless Recoveries∗

Kathryn KoendersArizona State University

Richard RogersonArizona State University

October 10, 2004

Abstract

This paper proposes a new explanation for the apparent slow growth inemployment during the last two recoveries. Our explanation emphasizesdynamics within growing organizations and the intertemporal substitu-tion of organizational restructuring. A key implication of our analysis isthat recoveries from recessions following long expansions will have sloweremployment growth. Empirical analysis shows that the recovery whichbegan in 1970 also exhibited slow employment growth, consistent withthis prediction of the analysis.

∗This paper was prepared for the 2004 St. Louis Federal Reserve Bank Economic PolicyConference on “Productivity, Labor and the Business Cycle”. Rogerson acknowledges supportfrom the NSF.

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1 IntroductionSince the work of Burns and Mitchell (1946), economists who study businesscycle fluctuations typically refer to the “business cycle facts” without need toreference a particular episode in a particular country. One of the acceptedstylized facts of business cycle movements is that employment and output arestrongly positively correlated, although employment lags output by about onequarter. The apparent slow growth of employment in the recoveries followingthe last two US recessions (i.e., the so-called “jobless recovery” phenomenon)runs counter to this stylized fact. This paper suggests a possible explanationfor this apparently anomalous behavior.The two most recent recessions in the US share a common property: both

followed unusually long expansions. Motivated by this observation we proposean economic mechanism that links the speed with which employment increasesduring the recovery from a recession to the length of the expansion precedingthe recession. The mechanism stresses the manner in which organizations seekto eliminate unneeded labor and is easily described. We assume that ineffi-ciencies regarding the use of labor emerge over time within an organization.Eliminating these inefficiencies (a process we refer to as reorganizing) requiresscarce organizational resources that must be diverted away from current produc-tion. This tradeoff generates opportunities for intertemporal substitution andwe show that reorganization will be postponed to periods in which production isrelatively low. It follows that after a long expansion, many more organizationshave postponed reorganization. Because reorganization leads to the sheddingof unnecessary labor and takes time, this gives rise to an extended period inwhich the economy sheds labor, thereby delaying the date at which aggregateemployment begins to increase during the recovery.The first part of this paper presents one formulation of a model of organiza-

tions that generates these effects. The core model should be seen as an extensionof the Lucas (1978) span of control model and the Hopenhayn (1992) industryequilibrium model to allow for a richer set of dynamics within an organization.Although we focus on the implications for business cycles, we believe this modelmay also prove useful for examining plant and firm level dynamics more gener-ally. The model is purposefully simplified in order to highlight the key economictradeoffs, and the analysis focuses on the qualitative nature of the interactions.We leave the task of building a model suitable for quantitative analysis of theforces for future work.Any theory that links the speed of the recovery in employment to the length

of the preceding expansion would seem to be a viable candidate for explainingthe anomalous behavior of employment following the last two recessions. How-ever, since the recession of 1969-1970 also followed an unusually long expansion,an obvious implication of any such theory is that a slow recovery of employmentshould also have been observed following this recession. The second part of thepaper turns to this issue and argues that when viewed from the perspectiveof our model, the behavior of employment in the 1970 recovery is in fact verysimilar to the behavior of employment in the recoveries of 1991 and 2001, and is

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qualitatively different from the behavior of employment in the other post WWIIrecoveries.One interpretation of our explanation is that the recent recessions do not

represent counterexamples to the standard set of business cycle facts, but ratherthat the business cycle facts need to be modified somewhat to acknowledge thatrecoveries following long expansions exhibit somewhat different dynamics. Thereare of course, other types of explanations that one might appeal to. For example,if one thought that it is only the two most recent recessions that appear different,one might consider the possibility that the business cycle facts are evolving andseek to understand what features of the economy are changing that would leadto the change in business cycle dynamics of employment. Schreft and Singh(2003) pursue this tack, arguing that increased flexibility in personnel policiesare responsible for the change. A second general class of explanations is to positthat the anomalous behavior of employment in any particular cycle is due to anadditional shock or policy change that happens to coincide with the recovery.The work of Cole and Ohanian (2004) on employment during the second halfof the Great Depression is exactly this type of explanation—they argued thatemployed did not recover as one would have expected because of the adoptionof the New Deal Policies and how they affected real wage rates. A third andrelated class of explanations stresses that trends in the economy change overtime and that cyclical properties may be affected by the nature of the trendchanges in the background. Along these lines a commonly heard explanationfor the recent slow recovery of employment was that the world had becomemore uncertain, leading firms to postpone increases in employment. Groshenand Potter (2003) is an example of this class. They argue that the underlyingamount of reallocation of labor across firms is currently greater and that thisaffects the pace of employment growth during the recovery. We do not carryout any comparison of our explanation versus these others, but do note that theextent to which the 1970 recovery is viewed as being similar to the two mostrecent recoveries would cast some doubt on the theory that their is evolution inthe business cycle facts.The mechanism that we describe is related to others that have appeared

in the literature, and it is of interest to note the similarities and differences.An old idea in the business cycle literature is that recessions are periods ofrestructuring. However, modern formulations of this, such as Lilien (1982), arebased on the notion that the key element of restructuring is across organizations,in particular, that resources need to be reallocated across sectors. In contrast,our model does not stress the reallocation of resources from one organizationto another but rather the restructuring that takes place within organizationsthat leads to the elimination of wasteful employment. Hall (1991) argued thatrecessions should be thought of as reorganizations, but the reorganizations thathe stresses were really reallocations of labor across activities. As noted above,Groshen and Potter (2003) have stressed that the amount of reallocation neededmay vary over time and be higher in some business cycle episodes than in others.A second related literature is associated with the work of Caballero and

Engel (1999) and Krusell and Smith (1998). Both papers consider the possi-

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bility that the distribution of individual state variables can influence how theeconomy responds to shocks. Caballero and Engel argue that the distributionof the difference between plant-level capital stocks and their ideal points wasquantitatively significant for the response of the economy to shocks. Krusell andSmith examine how the distribution of asset holdings across consumers affectspropagation of shocks. Qualitatively, our model emphasizes a similar channel,since we argue that the distribution of efficiencies of organizations matters forhow the economy responds to shocks. However, despite the similarity the me-chanics are quite different. In particular, if carried over to the labor setting,the Caballero and Engel model cannot explain why aggregate demand for laborwould continue to decrease in the face of positive aggregate shocks, a result thatcan emerge in our model and is central to accounting for the delayed increasein employment that accompanied the last two recoveries.An outline of the paper follows. In Section 2 we describe our benchmark

model, which captures the evolution of an individual organization over its life-cycle. In Section 3 we consider how aggregate temporary shocks interact withthe decisions of the organization, and derive our key result, which is that or-ganizations will concentrate reorganizations during periods with low aggregateshocks. Section 4 discusses the implications of this finding for the cyclical prop-erties of labor demand. Section 5 carries out an empirical analysis of postwarbusiness cycles and shows that the recovery following the 1969-1970 recessionexhibits patterns for employment that are quantitatively very similar to thosefound in the two most recent recoveries. Section 6 concludes.

2 Benchmark Model: A Life Cycle Model of Or-ganizational Dynamics

In this section we formulate a model of the life cycle of an organization. In thenext section we will use this benchmark model to investigate how the resultingpattern of organizational dynamics may be affected by shocks that we interpretto be business cycle shocks. The goal of these two sections is to highlighta particular interaction between organizational dynamics and business cycleshocks.1 With this in mind, we purposefully work in a very simple setting inorder to best highlight this interaction. We leave the development of a modelthat would be useful for a quantitative assessment of these interactions to futurework.The essence of benchmark model is as follows. We view an organization

as producing a differentiated product and therefore facing a downward slopingdemand curve for its product. Our model captures the following stylized evolu-tion of an organization over its lifecycle—when an organization is first created itfaces a relatively low demand for its product. But, over time this situation maychange. Some organizations fail and disappear, while some others experience

1Our model without aggregate shocks can also be viewed as extending the model of Hopen-hayn (1992) to consider richer decision making processes within organizations.

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large increases in the demand for their product and hence grow. However, eventhose organizations that grow and become large will at some point experiencedecreases in their demand and eventually cease to exist.The model that we describe below is a model of an individual organization

that faces stochastic demand for its product, but takes all input prices as given,where these prices remain constant over time. We assume that the organizationmaximizes the present discounted value of profits using a discount rate of β,which one can think of as one divided by one plus the interest rate. We nowdescribe the specifics of the model in more detail.

2.1 Demand

Let P (yt, εt) be the inverse demand faced by the organization in period t, whereyt is the amount of output produced in the current period and εt is a stochasticshock to the demand for the output of the organization. For a given value ofεt we assume that this function is twice continuously differentiable and strictlydecreasing in y, that the product P (y, ε)y is strictly concave in y, and satisfiesthe boundary conditions:

limy→0

d

dyP (y, ε)y =∞, and lim

y→∞d

dyP (y, ε)y < 0.

The first condition will ensure that an organization that remains in existencewill always wants to produce a positive amount of output, while the secondcondition says that output can effectively be viewed as bounded for any givenε, since the organization will never produce beyond the point where revenuesare decreasing in output.We assume a very simple form of the stochastic process on ε. In particular,

we assume that εt takes on only one of two values, εs and εl, where εs < εl,with the interpretation that εs is the demand state that will give rise to asmall organization, while εl is the demand state that will give rise to a largeorganization. To generate the standard life cycle profile of organization size,we assume that when an organization is first created it will have a value of εequal to εs, and that over time the state of demand may increase to εl. Wesimplify this process by assuming that the probability that ε increases from εs

to εl is given by the value πl, which is assumed to be constant over time. Wealso assume that the process never transits from εl back to εs. To capture thenotion that state εl is better than state εs, we assume that P (y, εl) > P (y, εs)for all positive values of y and that d

dyP (y, εl)y > d

dyP (y, εs)y for all positive y

as well.If the stochastic evolution of ε described above was a complete description

of the uncertainty facing a given organization, then all new organizations wouldeventually become “large” and remain that way forever. We incorporate the factthat organizations do not last forever by assuming that organizations face anexogenous probability of death, and that this probability varies with the stateof their demand, ε. In particular we assume that a organization with demandstate εi faces a probability λi of death. This assumption implies not only that

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organizations do not last forever, but also that not all new organizations willnecessarily become “large”.2 We assume that the realizations of the randomvariables are independent.Our assumption about timing is as follows. An organization that produced

in period t with demand state εi finds out the realizations of the demand anddeath shocks at the beginning of period t+1 but before any decisions are madein period t+ 1.

2.2 Production

We assume that labor is the only factor of production. The production technol-ogy in our model has several key features, which we detail in several steps.

2.2.1 Scale Effects

First, we assume that there are different ways to organize production, and thatthe optimal way to organize production is dependent upon the scale of pro-duction. In general one could imagine a large set of possible ways to organizeproduction, but given that we are restricting attention to a model with two de-mand states we also assume that there are only two ways in which productioncan be organized. We refer to each different way to organize production as adistinct technology. We let hi(y) denote the labor necessary to produce outputy using technology i. Because we will implicitly restrict parameter values sothat an organization with demand state εs will always use technology 1 whilean organization with demand state εl will always use technology 2, we will alsouse s and l to index the two technologies. The idea is that technology one isbetter if producing at a low scale, while technology two is better at producing ata large scale. We adopt the following functional forms for the two technologies.We assume that hs(y) = asy for all positive values of y, where as > 0. Theother technology is only operable above some minimum threshold scale y, andfor y ≥ y we assume that hl(y) takes the form hl(y) = aly, where al < as. Moregenerally we could specify that this technology can operate at scale less thany but that the average product of labor is sufficiently low that no one wouldchoose to operate it below the scale y. We assume free disposal of output, im-plying that an organization could choose to operate the large scale technologybut only sell a fraction of the output, though in our analysis we will implicitlyassume that this never happens.We assume that the organization hires labor in a competitive market and

hence takes the wage rate as given. In what follows we normalize the wage rateto one.

2This specification amounts to assuming that there are three demand states, with the thirdstate being an absorbing state in which the organization cannot sell any positive amountof output and still receive a positive price. We identify this third state with death of theorganization.

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2.2.2 Organizational Waste

An important goal for any organization is to use its resources efficiently. Thelarge differences in measured productivity across organizations suggests thatorganizations vary in the degree to which they accomplish this. Inefficient useof resources may take several forms. We incorporate one particular form ofinefficiency, which we refer to as waste. What we have in mind is that in anyorganization there is potentially some duplication of effort or unnecessary tasksbeing performed which affect labor productivity in an inframarginal way. Inparticular, in the context of the technologies described in the previous sectionwe assume that an organization with waste φ has labor requirement h(y) + φrather than h(y). The key feature of this waste is that it affects average laborproductivity but not marginal labor productivity. One could obviously considerinefficiency that also serves to alter the slope of h(y). Inefficiencies of this formare certainly plausible. We assume inefficiency only of the form as characterizedby the parameter φ because it is this type of inefficiency that will be central toour analysis. Alternative types of inefficiencies can be added to the analysis. Wenote as a matter of interpretation that we interpret this inefficiency as reflectinginefficiency in the organizational design and not inefficiency due to a workerthat is shirking, for example.For our purposes there are two key issues associated with these inefficien-

cies. The first is where they come from, and the second is how organizations caneliminate them. Again, our formulation will be somewhat specialized in orderto isolate a particular effect. In general one could imagine that inefficienciesstochastically occur within any organization, and that it takes organizationalresources to get rid of them. One could also assume that organizations devoteresources to these activities ex ante in order to reduce the likelihood that theyarise. Our formulation relies on the notion that changes in organizational scaleare likely to be associated with the appearance of inefficiencies since the orga-nization is less likely to know how to best use resources as it moves to a neworganizational structure.3 Motivated by this idea, we assume that all organiza-tions operating the small scale technology do so efficiently, but that wheneveran organization switches from the small scale technology to the large scale tech-nology it will necessarily move to a positive level of inefficiency that we denoteby the parameter φ. That is, if an organization used technology s in period t−1and switches to technology l in period t, then their labor requirement functionwill be aly + φ for y ≥ y. We note that it would be straightforward to also as-sume that a new organization that is operating the low scale technology for thefirst time also begins with an inefficiency, but we abstract from this possibilityfor simplicity. We assume that the level of inefficiency is known to the organiza-tion. While one could consider interesting issues that arise from organizationsnot having complete information about the state of their efficiency and needingto learn over time about them, we abstract from them here.Having described how inefficiencies arise, we now turn to the issue of how3Bertschek and Kaiser (2001) present evidence from a data set of German firms that changes

in productivity are linked with changes in organizational structure.

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an organization can get rid of them. We adopt a simple and straightforwardformulation. In particular, in any given period an organization makes a dis-crete decision about whether to try to eliminate inefficiency. Having done so,with probability πe the organization will decrease its inefficiency to zero in thefollowing period, while with probability 1− πe the organization will experienceno change in its level of inefficiency. Assuming that there is no improvementin efficiency the organization can continue to choose to try to get rid of theinefficiency in each subsequent period.Our formulation assumes that a given organization makes stochastic transi-

tions between two levels of efficiency. If we had a large number of organizationsall with inefficiency φ and they all continued to choose to try and eliminatethis inefficiency until successful, then the average level of inefficiency amongthis group of organizations would decrease monotonically and approach zeroasymptotically. As we will see later in the analysis, this is the pattern that wewant to generate. Of course, this pattern could also be generated by havingeach individual organization experience a monotonically decreasing level of in-efficiency rather than the all or none form that we specify. We have chosen theall-or-nothing form of improvements to simplify the analysis of the model.In the next subsection we describe in more detail the cost to the organization

of trying to reduce its level of inefficiency. Note that we assume that there is nodirect cost associated with changing from one technology to another. It wouldbe straightforward to add such a cost but it is not central to the effects that westress below. Lastly, our model is related to models of costly adjustment andmodels of organizational capital, so it is of interest to remark on these relation-ships. At a general level, the inefficiency associated with change of scale canobviously be interpreted as a form of adjustment cost. We note however, thatour specification differs from most specifications of adjustment costs becausethe cost does not necessarily disappear in the periods following the adjustment.That is, most models of adjustment costs assume a one time cost associatedwith the adjustment, but here the cost is permanent unless the organizationtakes some actions. The restructuring that takes place within organizations inour model can also be interpreted as a form of investment in organizationalcapital. However, our model differs from many formulations of organizationalcapital in that we implicitly assume that this investment in organization capitalis a substitute for labor input since it leads to a reduction in labor, while mostanalyses assume that increases in organizational capital lead to increases in themarginal product of labor.

2.2.3 The Role of the Manager

We assume that each organization has one manager and potentially many work-ers. The labor requirement functions described in the previous subsection shouldbe thought of as specifying the required amount of non-managerial labor input.In this regard our model is similar to the standard span of control model ofLucas (1979). However, we deviate from that model by allowing a manager tochoose between two primary uses of their time. In particular, we assume that

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a manager can either devote their time to facilitating production, or to tryingto reduce inefficiency. We shall cast this choice as having the manager choosebetween “producing” or “reorganizing”, which we will denote as m = p andm = r, respectively. The cost of having the manager devote their time to reor-ganizing is that they are not able to focus on production. We model this costas a decrease in the efficiency of labor used in the organization. In particular,we assume that if a manager of an organization using a large scale technologydevotes their time to reorganization, then the labor requirement function be-comes (1 + η)hl(y) where η > 0 is the efficiency loss associated with havingthe manager not focus their attention on production. The benefit of having themanager focus on reorganizing is that it makes it possible for the organizationto be more efficient in the future. As this description makes clear, a key tradeoffthat a manager faces when making their time allocation decision is between cur-rent efficiency and future expected efficiency. As we will see in the next section,it is this tradeoff and how it interacts with business cycle shocks that is at theheart of our analysis.We assume a competitive market for (homogeneous) managers. The orga-

nization will therefore also take the managerial wage as given, which we alsoassume to be constant over time. Because an organization cannot function with-out a manager, managerial compensation is effectively a fixed per period costfor the organization. We denote this wage by wm. The only way that an or-ganization can avoid having to hire a manager is to cease to exist. We assumethat if an organization chooses this option that it cannot return in the future.

2.3 The Organizational Life Cycle

It is straightforward to formulate the optimization problem of the organizationjust depicted. We do it recursively. The state vector for the organization thatremains alive is denoted by s = (ε, φ) where ε is the state of demand for itsproduct and φ is its level of inefficiency if it chooses to operate the large scaletechnology. An organization is always born into the state (εs, φ), which is to saythat a new organization begins with demand in the low state and an inefficiencylevel of φ. Note that the level of inefficiency begins at φ because if a neworganization were to use to large scale technology it would be faced with theinefficiency. But, as noted earlier, as long as it chooses to operate the low scaletechnology it can do so without experiencing any inefficiency. In each period,after observing its current state variable, if the organization remains alive itfaces three choices: which technology to use (i = s or l), how much outputto produce (y), and how to allocate the manager’s time (m = p or r). Giventhe organization’s state vector and choices for each of these decisions, we candetermine the current revenues net of payments to nonmanagerial labor thatwould accrue to the organization, which we will denote by R(ε,φ,i, y,m). Thisfunction takes the following form:

R(ε,φ, i, y,m) = P (y, ε)y − (1 + ηIm=r)hi(y)− Ii=lφ− wm (1)

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where Im=r is the indicator function for m = r (i.e., the manager reorganizes),and Ii=l is the indicator function for using the large scale technology.It is now easy to write the Bellman’s equation for the maximization problem

faced by the organization:

V (ε,φ) = max{0,maxi,y,m

[R(ε,φ, i, y,m) + β(1− λi)EV (ε0,φ0)]} (2)

where the outer max reflects the decision of whether or not to remain active,and the inner max reflects the optimal choices assuming that the organizationremains active. We have assumed that if the organization ceases to exist, eitherthrough choice in the current period, or because of a death shock in the nextperiod that all future returns will be zero. The expectation operator E incor-porates two elements. First, it incorporates the dynamics in the demand stateε, and second, it incorporates the dynamics in the level of inefficiency if theorganization chooses to have the manager devote their time to reorganization.Given our assumptions thus far, we cannot rule out some rather extreme or

degenerate outcomes that are of little interest. We describe some of these now.In what follows we do not offer any specific conditions on the model specificationto rule out these outcomes, but do note intuitively what parameters would berelevant in ruling out certain outcomes.It is possible that a newly created organization cannot earn positive expected

lifetime profits and hence will choose to shut down. In particular, as noted pre-viously the managerial wage acts like a fixed cost of being in operation, and itis well known that in a model with a fixed cost, it is not enough to guaranteepositive net revenues from the variable factors, as our earlier assumption on Pdoes. Of course, if a newly created organization is choosing to shut down andthere is some cost associated with creating an organization in the first place,then this would imply that new organizations are never created. In an equi-librium context in which consumption is infinitely valued at the margin whenconsumption is zero, such an outcome could not be an equilibrium outcome. Inview of this, it is natural to assume that wages are sufficiently low relative tothe price of output that this is not the outcome. Given our assumptions onthe price function P , it follows that if the expected present discounted value ofprofits are positive for a newly created organization, then they are positive forany feasible state vector. This does not necessarily imply that the organizationwill have positive current period profits in all states—it is possible that a neworganization only remains active because of the possibility of transiting to thehigher demand state and that the higher demand state is the only state that isprofitable in a static sense. However, given our assumptions on P it is true thatconditional on remaining active, an organization will always choose to producea positive amount of output, even if current period profits were to be negative.The model has been constructed to focus on the change in scale of production

and the associated change in organization structure that occurs as organizationssuccessfully mature. However, given a demand function P , if the value of y issufficiently large then no organization will ever choose to operate the large scaletechnology, and if y is too small then all organizations will choose to operate

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the large scale technology. In the context of our model, neither of these cases isparticularly interesting. So, in what follows we assume that it is optimal for anorganization in demand state εs to operate the low scale technology and for anorganization in the demand state εl to operate the large scale technology. Wenote, as a feature of our specification, that it is not possible to eliminate futureinefficiency while currently operating the small scale technology. It follows thateven if an organization decides to reorganize and thereby experiences the currentloss of efficiency associated with η, that the organization will still choose tooperate the large scale technology.Lastly, it is also possible that the values of φ and η are such that no or-

ganization would ever choose to reorganize. This could happen if the level ofinefficiency (i.e., φ) is sufficiently small relative to the foregone productivity(i.e., η is large) or the probability of failure in reorganization (i.e., 1−πe). Con-versely, if the size of the inefficiency is sufficiently large relative to the cost ofeliminating it, then an organization would always choose to reorganize. Sincethe case of no reorganization is not very interesting in the context of our model,we assume in what follows that we are in a region of parameter space in whichorganizations do sometimes choose to reorganize.Conditional on assuming that a newly created organization chooses to re-

main in existence, that organizations in the low (high) demand state operate thelow (high) scale technology, and that organizations sometimes choose to elim-inate inefficiency, it is fairly easy to characterize the life cycle dynamics thatemerge. In particular, any newly created organization will operate the low scaletechnology and hire an amount of labor that we denote by hs, and producesoutput denoted by ys. Over time there are three things that may happen tothis organization. It may receive a shock and cease to exist, it may remain inthe same position and hence continue to hire hs workers, or it may experiencea shock that increases its demand to the high state.If it is sometimes optimal to try and eliminate inefficiency, then because the

organization’s problem is recursive, it must be optimal to do it the first timethe organization reaches the high demand state. While in the high state andreorganizing, the organization is employing the large scale technology and hireslabor that we denote by hr, producing an amount of output that we denote byyr. Even though the manager is devoting time to reorganizing and this lowersthe marginal product of labor, it still must be the case that hr > hs. To see thisnote the following. First, this organization must be producing at least y units ofoutput and this must exceed the amount of output produced in the small demandstate, or else it would not have been optimal to use the low scale technology inthe low demand state. Now, if it was possible to produce more output with lesslabor, then the organization could have chosen this combination in the previousstate and chosen not to sell all of the output produced. It follows that hr mustexceed hs. It follows that if an organization experiences an improvement in itsdemand state, it increases both its labor input and its output. Note that wecannot say anything about what happens to average labor productivity. Thiswill depend on the magnitudes of the parameters η and φ.An organization in the large demand state that is reorganizing can in turn

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experience three different transitions. First, it may receive a bad shock and ceaseto exist. Second, it may be unsuccessful in eliminating inefficiency and remainin the same state, in which case it chooses the same actions again. Third, it maybe successful in eliminating the inefficiency. We denote the levels of y and h thatresult in this case as hl and yl. How do the values of hl, yl, and yl/hl comparewith the corresponding values from earlier in the life cycle? The first ordercondition for current period choice of output combined with our assumptionson P imply that output will definitely increase when the manager focuses onproduction rather than reorganization. This is because the term (1 + η) goesaway from the first order condition. However, it is ambiguous whether this leadsto an increase or decrease in h, for two reasons. First, even if the only effect werethe improved efficiency associated with the managerial time allocation, the effecton labor, as opposed to output, will depend upon the elasticity of the demandfunction. Second, the elimination of the inefficiency measured by φ necessarilyimplies a decrease in labor in the amount of φ. However, although the effecton h is ambiguous, it is easy to see that independently of what happens to h,average labor productivity will necessarily increase.Although with our implicit assumptions on parameter values that the orga-

nization will never choose to postpone reorganization once it reaches the largedemand state, we can still ask what levels of h and y would be optimal if it choseto do so. Denote these levels by hp and yp. We ask how hp and hl compare.In making this comparison we are assuming that the current period marginalefficiencies are the same since in both cases the manager is focusing on produc-tion. Given our formulation, it follows that output will be the same in eachcase., i.e., yp = yl. However, because of the waste in the former case, we knowthat hp > hl. This will be of particular interest later on because it says thatan inefficient firm that chooses to postpone reorganization will necessarily shedworkers in the future.As a final remark in this section, we note that our model emphasizes the

restructuring that accompanies growth of an organization. It seems equallyplausible that restructuring within shrinking organizations would also be ofimportance. For the implications that we stress we believe that similar resultswould emerge from this situation as well, so we have chosen to focus on growingorganizations purely for simplicity.

3 The Model With Temporary ShocksThe previous model considered the decision making of an organization over itslifecycle. The only shocks in that model were highly persistent, and we inter-preted them to be organization specific. In this section we add purely temporaryshocks to the model and examine how these temporary shocks influence the lifecycle dynamics that we studied earlier. Although our model is purely deci-sion theoretic, we will interpret the iid shocks that we introduce as reflecting(aggregate) business cycle shocks.Formally, we assume a second shock that influences demand, and for sim-

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plicity we assume that this shock is multiplicative, so that we write the inversedemand function facing the organization as ε2tP (yt, ε1t) where P is the samefunction as described earlier, ε1t is the shock that we previously labelled as εt,and ε2t is an iid shock that is drawn from a distribution with cdf F (ε2). Weassume that realizations of ε2 lie in the interval [εmin, εmax] and that this in-terval contains 1 in its interior. Note that if ε2t = 1 for all t then the modelis identical to that considered previously. All other aspects of the environmentare left unchanged.Proceeding as before, we define the revenue associated with decisions in a

particular state as R(ε1, ε2,φ,i, y,m). This function takes the following form:

R(ε1, ε2,φ, i, y,m) = ε2P (y, ε1)y − (1 + ηIm=r)hi(y)− Ii=lφ− wm (3)

where Im=r is the indicator function for m = r (i.e., the manager reorganizes),and Ii=l is the indicator function for using the large scale technology. It isimmediate that both R and Ry are increasing in ε2.It is again easy to write the Bellman’s equation for the maximization problem

faced by the organization:

V (ε1, ε2,φ) = max{0,maxi,y,m

[R(ε1, ε2,φ, i, y,m) + β(1− λi)EV (ε01,ε02,φ

0)]} (4)

For future reference it is worthwhile to elaborate on the expected value term inmore detail. As noted earlier, this expectation takes into account the evolutionof the exogenous shocks as well as the evolution of the inefficiency variable inresponse to the decision about reorganization. If ε1 = εs then the only value ofφ of interest is φ = φ. Assuming this configuration plus an arbitrary value forε2, the term for next period’s value in the Bellman equation becomes:

β(1−λi)EV (ε01,ε02,φ0) = β(1−λs)[πlZV (εl, ε, φ)dF (ε)+(1−πl)

ZV (εs, ε, φ)dF (ε)]

(5)If the organization has ε1 = εl, then the only efficiency value of interest is stillφ = φ, since otherwise there is no need for a decision about reorganization andthe problem becomes static. For an arbitrary value of ε2 if the organizationdecides to reorganize, then the future term in the Bellman equation becomes:

β(1−λi)EV (ε01,ε02,φ0) = β(1−λl)[πeZV (εl, ε, 0)dF (ε)+(1−πe)

ZV (εl, ε, φ)dF (ε)]

(6)whereas if it chooses not to reorganize then the same term becomes:

β(1− λi)EV (ε01,ε02,φ

0) = β(1− λl)

ZV (εl, ε, φ)dF (ε) (7)

As was true in the previous subsection, depending upon parameter valuesthere are various forms that the optimal decision rules may take. We modify

13

our previous assumptions marginally so we now assume that when ε1 = εs theorganization will choose to remain active independently of the value of ε2.4 Wefurthermore assume that when an organization experiences an increase in itsdemand state from εs to εl that there is at least some interior value of ε2 forwhich the organization would choose to reorganize.Finally, we also place an implicit assumption on the size of the shocks to

ε1 and ε2. In particular we assume that life cycle shocks are much larger thanbusiness cycle shocks. The significance of this is that we assume that whenε1 = εs that the organization does not wish to operate the large scale technologyindependently of the realization of ε2. Similarly, we assume that when ε1 =εl that the organization never chooses to operate the small scale technologyindependently of the realization of ε2. This model is identical to the model ofthe previous section if we assume that εmin = εmax = 1. It follows that if theprevious model implies technology i is only operated in demand state i, thatthis model will also generate this result if the range of ε2’s is not too large.We are now able to prove our main result, which is that the decision to

reorganize when in state (εl,ε2,φ) is characterized by a reservation value ofε2, with the property that it is optimal to reorganize if ε2 < ε∗2, and not toreorganize if ε2 > ε∗2. The intuition for the result is simple: it basically reflectsintertemporal substitution of reorganization. Reorganization imposes a costtoday in terms of foregone efficiency of labor, but offers a future gain in reducingwaste. If ε2 is iid, then future gains are the same independently of the currentvalue of ε2. But, we will show that the current period cost of reorganizing isincreasing in the amount of production desired in the event of not reorganizing,which in turn is increasing in ε2.We now establish these results. Consider an organization in state (εl,ε2,φ).

Let yp denote the optimal level of production if the organization were to choosenot to reorganize, and let yr denote the optimal level of production were theorganization to choose to reorganize. Conditional upon deciding whether toreorganize, note that the resulting decision about the optimal choice of y isstatic, and can be represented as:

W (ε2, η) = maxy{ε2P (y, εl)y − (1 + η)h(y)} (8)

where η takes on the value 0 in the event of m = p, and η = η in the event thatm = r. We denote the optimal choice of y as y(ε2, η). Note that the first ordercondition that defines this function is:

ε2[yP1(y, εl) + P (y, εl)] = (1 + η)h

0(y) (9)

Given our assumptions it follows trivially that the optimal value of y is increasingin ε2 and decreasing in η.Let V p(εl, ε2, φ) and V r(εl, ε2, φ) be the resulting optimal values obtained

from choosing not to reorganize and to reorganize, respectively, assuming that4More generally it would be straightforward to allow for the possibility that the organi-

zation will not remain in operation for all realizations of ε2. In this case there will be areservation value of ε2 that dictates whether the organization remains.

14

output is chosen optimally in each case. Now consider the difference betweenthese two values. Using V p and V r to denote these functions, direct substitutiongives:

V p(εl, ε2, φ)− V r(εl, ε2, φ) = Rp −Rr + β(1− λl){ZV (εl, ε, φ)dF (ε) (10)

−[πeZV (εl, ε, 0)dF (ε) + (1− πe)

ZV (εl, ε, φ)dF (ε)]}

where we have written Rp = R(εl, ε2, φ, l, yp, p) and Rr = R(εl, ε2, φ, l, y

r, r).Note that the value of the terms involving integrals are all independent of ε2.Denote these terms by the constant A. Moreover, the difference in the tworevenues can be reduced to:

Rp −Rr =W (ε2, 0)−W (ε2, η) (11)

It follows that equation (10) can be written as:

V p(εl, ε2, φ)− V r(εl, ε2, φ) = [W (ε2, 0)−W (ε2, η)] +A (12)

This equation is intuitive. The term in square brackets is the current periodcost of reorganizing: it represents the loss in current revenue associated withhaving the manager devote their time to reorganizing. The term A is the futurebenefit to reorganizing. Given our assumption, this is simply a positive numberthat is independent of ε2.We can now easily show that this difference is increasing in ε2. It is sufficient

to show that the term in square brackets is increasing in ε2. Differentiation give:

d

dε[W (ε2, 0)−W (ε2, η)] =W1(ε2, 0)−W1(ε2, η), (13)

so it is sufficient to show that W12 < 0. By definition,

W (ε2, η) = ε2P (y(ε2, η))y(ε2, η)− (1 + η)h(y(ε2, η)) (14)

Using the envelope condition, we have that

W2(ε2, η) = −h(y(ε2, η)) < 0. (15)

It then follows that

W12(ε2, η) = −h0(y(ε2, η))y1(ε2, η) (16)

Since h is increasing and the solution for y is increasing in ε2, it follows thatW12 < 0 and hence V p(εl, ε2, φ)−V r(εl, ε2, φ) is increasing in ε2. If the benefitto not reorganizing is monotone in ε2 it follows that the optimal reorganizationstrategy is to employ a reservation value, as stated above.If the reservation value is equal to εmax, i.e., the upper support of the distri-

bution of the temporary shocks, then the organizational dynamics in this model

15

are qualitatively the same as in the previous subsection. That is, whenever asmall organization gets an improvement in their idiosyncratic demand state ε1,they immediately choose to reorganize and continue to do so until the reorga-nization is successful. Fluctuations in ε2 will lead to additional fluctuations intheir labor input and output, but the lifecycle dynamics will be similar.However, if the reservation value ε∗2 is interior to the interval [εmin, εmax],

then qualitatively different dynamics can emerge. In this scenario, if an orga-nization in the small idiosyncratic demand state receives a shock that raises itto the large idiosyncratic demand state, the organization may or may not de-cide to reorganize at that point. In particular, if ε2 is sufficiently high then theorganization will choose to postpone the decision to reorganize in order to takeadvantage of the current temporarily high demand. As stated earlier, the orga-nization will engage in intertemporal substitution of managerial actions. And,following from our discussion of the previous model, we know that an organiza-tion that chooses to postpone reorganization will necessarily employ less laborin the future when it does successfully reorganize, even holding the value of ε2constant.

3.1 Extension to the Case of Persistent Shocks

The previous analysis has assumed that the shock ε2 is iid over time. Of course,if one wants to think of the ε2 shock as proxying for business cycle movementsin the demand faced by an individual organization, then the iid assumption isnot very appealing. A well documented property of business cycles is that theyare persistent, in the sense that if the economy is above trend today then wealso expect it to be above trend next period. In view of this it is of interestto ask whether our result about the reservation value will extend to the case ofpersistent shocks. In fact, the argument is easily extended.In the iid case, we argued that the current cost of reorganizing is increasing

in the current value of ε2, and that the expected future benefit of reorganizing isindependent of the current period value of ε2. The first statement is independentof whether the realizations of ε2 are iid or not. However, a key observation aboutthe structure of our model is that the benefit to successful reorganization is infact independent of future realizations of ε2. The reason for this is that inour model successful reorganization does not impact on the marginal product oflabor, and as a result an efficient organization and an inefficient organization willchoose the same level of output conditional upon having the same managerialtime allocation. The only effect on profit is from saving labor in the amountof φ for each future period that the organization remains in existence, and thissaving is independent of all future realizations of ε2.The additional issue that needs to be addressed in the context of a model

with persistent shocks to ε2 is the following: An organization faced with acurrent realization of ε2 can also consider the possibility of waiting a periodto reorganize. If the benefit from waiting increases as ε2 decreases, then thereservation property might not be preserved. In the iid case the benefit fromwaiting is actually increasing in ε2, since next period’s expected one-period cost

16

of reorganizing is independent of ε2, so that a higher current value of ε2 indicateslower expected costs in the future, whereas a low value of ε2 indicates higherexpected costs in the future.With this in mind we can present the alternative characterization of the

decision to reorganize. In particular, let C(ε) = W (ε, 0) − W (ε, η) be thegain this period from not reorganizing. Let G = βπeφ/(1 − β(1 − λl)) be the(expected) gain from choosing to reorganize today. Letting H(ε) be the benefitof today’s managerial choice relative to reorganizing today, we have that H(ε)satisfies:

H(ε) = max{C(ε) + β

ZH(ε0)F (dε0, ε), 0} (17)

where the first term indicates the gain from not reorganizing today, and thesecond term indicates that if the manager chooses to reorganize then the gainis clearly zero. We know that C(ε) is increasing in ε from our previous analysis.If we knew that the term C(ε) + β

RH(ε0)F (dε0, ε) is increasing in ε, the cur-

rent realization of the shock, then we could easily conclude that the reservationproperty holds. Note as stated earlier that if ε is iid then the integral is indepen-dent of ε and the property holds based on the property of C. However, findingconditions under which the integral is increasing in ε is a standard problem indynamic stochastic models. In particular, if we assume thatZ

g(ε0)F (dε0, ε) (18)

is increasing in ε for any increasing function then we can easily show that thevalue function H will in fact be increasing and hence that the integral has thedesired property.Loosely speaking, a process for ε2 that implied mean reversion would tend to

satisfy this property. This is because a high value of ε2 today implies that futurevalues of ε2 will be lower, implying that it is beneficial to wait to reorganize.On the other hand, a very low value of ε2 today implies that future values ofε2 will be higher, implying that there is greater incentive to reorganize todayrather than in the future.We conclude that the reservation value property for the optimal reorgani-

zation decision will also hold in the case of persistent shocks under reasonableconditions.

4 Implications for Business Cycle DynamicsOur formal analysis has only considered the decision problem of an individualorganization that takes demand for its product as given, assuming that wagesfor workers and managers and the real interest rate are constant over time. Sucha model can be cast in an industry equilibrium setting such as Hopenhayn andRogerson (1993) in which case the organizational dynamics that we describecan capture the steady state dynamics of general equilibrium model in which

17

all shocks are idiosyncratic, i.e., there are no aggregate shocks. If one intro-duces aggregate shocks into such a model, then one would need to take intoaccount the effect that these shocks have on wage rates and the real interestrate. Veracierto (2002) and Thomas (2002) are examples of models in whichthese general equilibrium effects are considered. Hence, in its current form themodel is really not appropriate to discuss how the economy responds to aggre-gate shocks. Nonetheless, in this section we want to discuss what our previousanalysis suggests as some potential effects of interest for business cycle dynam-ics. We leave development of the appropriate framework and the associatedformal analysis for future work.Consider the following situation. We have a unit mass of entry of new

organizations each period, each of which enters into the individual state (εs, φ).We consider the ε2 shock to be common to all organizations while the ε1 shockis idiosyncratic, and trace out the evolution of the economy assuming that wagerates and the interest rate remain constant. The first observation that we wantto stress is that the aggregate state of this economy will be the realization ofthe aggregate shock ε2 and the distribution of organizations across individualstates. Entering a given period there are three types of organizations: those thatare in the state (εs, φ), (which we call state 1), those that are in the state (εl, φ)(which we call state 2),and those that are in state (εl, 0) (which we call state3). We let µi be the mass of firms in each of the three states. The evolution ofthe µi’s is affected by the realization of the aggregate shock since it determineswhether organizations in state 2 will be reorganizing, thereby influencing theprobability that an organization transits to state 3. In particular, let µit be thedistribution of active organizations in period t. Then, if ε2t > ε∗2, we have thefollowing:

µ1t+1 = (1− λs − πl)µ1t + 1 (19)

µ2t+1 = (1− λl)µ2t + πlµ1t

µ3t+1 = (1− λl)µ3t

If, on the other hand, we have ε2t < ε∗2 then the distribution will evolve accordingto:

µ1t+1 = (1− λs − πl)µ1t + 1 (20)

µ2t+1 = (1− λl − πe)µ2t + πlµ1t

µ3t+1 = (1− λl)µ3t + πeµ2t

Two simple conclusions can be drawn from these laws of motion. First, notethat the law of motion for µ1t is independent of the realization of ε2. It followsthat if entry is constant as we have assumed, that the value of µ1 will approach aconstant and will not be affected by realizations of ε2. The constant fraction oforganizations in state 1 is easily computed to be λl/(λl+πl). The second pointto note is that the remaining mass of organizations will be split between type2 and type 3 organizations, and that this division will depend upon the history

18

of the ε2 realizations. Specifically, if ε2 remains above ε∗2 then there is a greaterbuildup of organizations in the second state at the expense of organizations inthe third state. It follows that the longer the aggregate shock remains above thereservation value, the greater will be the buildup of organizations in the secondstate. In what follows, we illustrate the potential effects that this can have onhow the economy responds to subsequent shocks.

4.1 A Reduced Form Example

For present purposes, the most effective way to illustrate the interaction be-tween the distribution of organizations and the response of the economy to agiven sequence of aggregate shocks is with a very specific reduced form exam-ple. Consider an economy at time 0 with unit mass of organizations that aredistributed across types. We assume that the stochastic process for ε2 has asequence of realizations of the following form. In period 0 the economy is hit bya (very) negative value of ε2 but subsequent to this experiences a constant andgradual increase back towards its unconditional mean value. We assume thatit takes the economy 20 periods to reach this value, at which time it remainsthere. This type of realization could be thought of as tracing out the impulseresponse function in the presence of a mean-reverting process.We assume the following reduced form properties in our example. First, we

assume that reorganization is optimal for this entire range of realized ε2 values.Second, we assume that when an organization reorganizes successfully, the effecton labor input is a decrease of ef , holding ε2 constant and is independent ofthe level of ε2. Third, we assume that each period in which ε2 is increasing, theaggregate effect of this on labor input is an increase in labor input of eh which weassume is distributed across organizations according to size.5 We assume that inperiod 0 a small organization employs 10 workers and that a large reorganizedorganization employs 100 workers. By assumption, a large organization in theprocess of reorganizing will employ 100 + ef workers. The probabilities πl, πe,λs and λl are as before.Our goal here is to illustrate the potential for the initial distribution of orga-

nizations to influence the resulting response of employment to a given sequenceof shocks. With this in mind, we simulate the implied path of aggregate em-ployment for several different initial conditions. As already noted above, witha constant rate of entry of new organizations, asymptotically there will be aconstant mass of organizations and a constant fraction of them will be of type1 (i.e., in the small demand state with inefficiency φ). In view of this we alwaysconsider the initial fraction of organizations that are of type 1 to correspond tothis fraction. We normalize the total mass to equal one and hence assume thatµ10 = λl/(λl + πl). As noted earlier, however, at any given point the distribu-tion of the remaining organizations between type 2 and type 3 will be influencedby the previous history of realizations of ε2, and we therefore consider different

5One could interpret this reduced form as reflecting a log linearization of the individualdemand for labor functions.

19

0 5 10 15 20-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Period

Empl

oym

ent (

Dev

iatio

n fro

m M

ean)

mu2=.30mu2=.35mu2=.40

Figure 1: Effect of Initial Conditions on Employment

scenarios for how this remaining mass is allocated across type 2 and type 3organizations.For the paths shown in Figure 1 we have set eh = .1, and ef = 10. Setting

eh = .1 amounts to assuming that the accumulated increases in ε2 over the 20periods would increase aggregate employment by roughly 4% over the courseof twenty periods, holding all else constant. We set ef = 10, implying thatsuccessful reorganization leads to a reduction in employment of roughly 10%.Weset λl = πl = .0025, implying that over the course of the twenty periods theaccumulated probability of failure for large organization or success for a smallorganization is roughly 5 percent. Finally, we set πe = .05 which implies anexpected duration of 20 periods for successful reorganization. While we haveoffered these quantitative guides to thinking about the parameter selections, wealso emphasize that this example is intended purely as illustrative. We leavea rigorous quantitative assessment of the economic mechanisms described herefor future work.Figure 1 shows the employment paths that result for three different initial

values of µ2.In each case, the curve represents deviations from means for each path in

order to focus attention on the implications for timing. The figure shows thatas µ20 increases it takes longer to reach the turning point of employment. Thisresult is intuitive. The greater the value of µ20, the greater is the total amountof reorganization that needs to be done. As this reorganization takes place, suc-

20

0 5 10 15 20

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Period

Empl

oym

ent

fires, mu2=.30fires, mu2=.35fires, mu2=.40hires, all cases

Figure 2: Initial Conditions and Hiring and Firing

cessful organizations will be shedding labor. This labor shedding is an opposingforce to the increases in labor associated with the gradual improvement in theaggregate shock ε2. A key point to note is that in our model reorganization ispotentially a long-lasting process in the sense that in any given period only agiven fraction πe of the remaining reorganization will be carried out. In fact, itis interesting to note the implications of the extreme case in which πe = 1. Inthis case all of the “accumulated” reorganization will be carried out in the firstperiod and there will be a large drop in employment, but after this we will seea continual increase in aggregate employment as ε2 increases. Hence, a largeamount of accumulated reorganization will simply lead to a very large one timedrop in employment, but will not lead to a delayed turning point for aggregateemployment.To understand the dynamics of the opposing forces, the next figure shows

the time paths of firing and hiring for each of the three scenarios considered inFigure 1.6

In all three cases the hiring associated with the improvement in ε2 is constantover time and equal to .1. However, although each economy has the samefundamentals, the fact that the initial distribution of µ varies implies that thetime path of fires associated with successful reorganization will be different. As

6An organization that successfully reorganizes may of course choose to fire fewer than 10workers and not hire any new workers, so measured hiring and firing in the economy may notreproduce these curves.

21

the graph shows, the curves are effectively parallel shifts of each other, withthe highest value of µ20 associated with the highest level of firing. Becausesuccessful reorganization takes time, the path of firing is fairly drawn out. Theimportant feature to note is that aggregate employment will continue to dropas long as the firing curve lies above the hiring curve. And since a higher valueof µ20 raises the firing curve but leaves the hiring curve unchanged it illustrateshow restructuring can influence the point at which aggregate employment beginsto increase.We should emphasize that the dynamics that we have just traced out are

obviously not definitive predictions of the model. As noted earlier, whetherreorganization leads to labor shedding depends on parameter values. The mainpoint that we want to emphasize is that the model suggests a mechanism whichcan produce these types of dynamics.

4.2 General Equilibrium Considerations

Although our analysis has only considered the decision problems of individualorganizations and then aggregated holding wage and interest rates constant, itis worthwhile to discuss how general equilibrium considerations would possiblyaffect the types of outcomes that we were emphasizing. In particular, it isimportant to emphasize this issue in the context of the literature related to thework of Caballero and Engel (1999) referred to in the introduction. In thatpaper, they argued that changes in the distribution of individual firm statevariables was important in influencing how the economy responds to shocks.However, the work of Veracierto (2002) and Thomas (2002) showed that ingeneral equilibrium versions of the model the effects of interest rate movementsbasically offset the partial equilibrium effects.There are two main issues that arise. The first concerns how changes in

prices might impact the incentives for intertemporal substitution in our deci-sion problem, as represented in our key analytic result showing the existence ofa reservation value of ε2 for the reorganization decision. With constant wagesand interest rates, reorganization will be shifted away from times of high eco-nomic activity and toward periods of low economic activity. If real wages wereprocyclical, they could generate an opposing force to our intertemporal sub-stitution. If wages are higher in periods of high economic activity and shocksare persistent then this produces a cost of not reorganizing that is procyclical.Simply put, the benefit of shedding labor is greater if wages are higher.General equilibrium effects could also operate through changes in the real

interest rate. However, if one views the case of procyclical real interest rates asthe case of primary interest, then this effect will actually reinforce our result. Ifcurrent real interest rates are high then current period costs are amplified andfuture benefits are attenuated, increasing the incentive to postpone reorganiza-tion in good times.One could plausibly argue that some other margins that we have assumed

to be constant over time would also exhibit variability over the cycle. Forexample, although we assumed that transition probabilities are constant over

22

time, one could argue that the probability of a small scale organization becomingsuccessful increases in good times, i.e., that πl is higher in good times. Thisby itself would tend to accentuate the effects that we have emphasized, sincethis will lead to a larger build up of type 2 organizations during good times.Similarly, if entry is higher in expansions then this will also tend to accentuatethe build up of type 2 organizations.A second issue that must be addressed in a more complete model is to

understand why the workers that are being released due to restructuring do notfind employment somewhere. One possible channel is standard intertemporalsubstitution effects. When an organization restructures, the shift of managerialtime away from production and toward restructuring leads to a decrease in themarginal product of labor. A second channel that is not in our model butwhich may be important, is that it could be that the organizations with thegreatest expected increases in employment in the future are those which haverecently experienced large increases. If this were true, it could be that theorganizations who decide to restructure are the same organizations that willeventually add the most workers. One could imagine a more detailed model inwhich an organization does not add to its existing labor force at the same timethat it is trying to reorganize. Hence, the decision to reorganize is implicitlya decision to postpone new hires. Lastly, if one were to imbed our model intoa model in which it takes time for workers to move from one organization toanother, then a long lasting increase in separations would also lead to a longlasting decline in employment.

5 A Closer Look at Jobless RecoveriesIn this section, we argue that the insights derived from the preceding discussionmay be relevant for understanding some features of business cycle dynamics,and that in particular they may be very relevant for the discussion of the phe-nomenon that has become known as the jobless recovery. As noted in the intro-duction, many individuals have coined the term “jobless recovery” to describethe apparent slow growth in employment following the troughs of the two mostrecent recessions in 1991 and 2001. Viewed in a broader perspective, the obviousimplication of such a description that not all business cycles are alike. This isan old an recurring theme in the business cycle literature. Burns and Mitchell(1946) were among the first to systematically measure the business cycle andargued that business cycles bear a remarkable similarity to each other alongmany dimensions. In particular, they developed the notion of a reference cycleto represent the “typical” business cycle. Influenced by this work, Lucas (1977)argued that a key stylized fact is that all business cycles are the same from theperspective of qualitative comovement of series. At the same time, there aremany instances in which researchers have argued that some particular businesscycle exhibits properties that distinguish it from its predecessors, while others

23

have argued that the business cycle phenomenon is slowly changing over time.7

The discussion of the previous section suggested the possibility that followingthe end of a long expansion it may take longer for employment to start toincrease once again. This argument is consistent with the fact that each of thelast two recessions has exhibited a relatively long period before employmentbegan to increase, since each of the last two expansions has been extremelylong by historical standards. However, there is another episode in the post warperiod which would seem to be relevant, and that is the recession of 1969-1970which also followed a very long expansion. If the channel that we point to isquantitatively important, then this period should also have produced a “joblessrecovery”. The goal of this section is to argue that the evidence is indeedconsistent with this prediction. In particular, we will argue that there are threerecessions in the post war period that stand out as distinct from the others interms of the dynamics for employment in the subsequent recovery: the 1969recession, the 1991 recession, and the 2001 recession. The material presentedhere draws on the results presented in Koenders (2004), which provides a muchmore thorough analysis.

5.1 A Review of Schreft and Singh

It is useful to begin with a summary of the analysis of Schreft and Singh (2003).They carry out the following calculation. They start with seasonally adjusteddata for employment from the establishment survey. They then identify the levelof employment at each of the NBER turning points that corresponds to the endof recessions. For each recovery, they plot the percentage change in employmentfrom the turning point that occurs over the subsequent twelve months. Figure3 below is equivalent to the picture that they produce except that we haveincluded the two recessions from the 1950’s in our analysis, and we have timeaggregated the employment data to quarterly frequency.But our Figure 1 tells the same story as Chart 1 in their paper. Whereas

the typical recovery shows steadily rising employment, with an increase of morethan 3 percent in the first year of the recovery, the two most recent recessionsshow employment decreasing in each of the four quarters following the turningpoint. While this picture certainly suggests that the two recent recoveries aredifferent than the average of the preceding ones, it obviously does not tell usif there are previous episodes that also resemble the two recent ones. For ourpurposes we are particularly interested in whether the recovery that began in1970 also displays this pattern. Figure 4 below repeats the analysis of Figure 3except we now consider three recoveries individually and compare them to theaverage of the remaining five recoveries. (Throughout this analysis we ignorethe recovery in the early 1980’s since it was so short-lived.)This figure suggests that the recovery that began in 1970 is much more

similar to the average recovery than it is to the recoveries following the two7A related but distinct issue is the extent to which business cycles have become less fre-

quent.

24

-2 -1 0 1 2 3 40.99

0.995

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

Quarters before and after the trough

Inde

x nu

mbe

r, tro

ugh

= 1

20011991average cycle

Figure 3: The Schreft-Singh Finding

-2 -1 0 1 2 3 40.99

0.995

1

1.005

1.01

1.015

1.02

1.025

1.03

1.035

Quarters before and after the trough

Inde

x va

lue,

trou

gh =

1

200119911970average cycle

Figure 4: The 1970 Recovery (Schreft-Singh Method)

25

most recent recessions. One can repeat this analysis for the other recoveries aswell, and one obtains a similar pattern in each case. Based on this analysis, onewould be lead to conclude that it is only the two most recent recoveries thathave had particularly distinctive employment dynamics.However, there are several issues that we want to raise regarding the Schreft-

Singh method of summarizing the data. The first issue is that the Schreft-Singhmethod is not consistent with modern views of the business cycle. Following Lu-cas (1977), modern business cycle analysis views the business cycle as deviationsfrom a slowly changing trend. Properties of business cycles should be propertiesof the component of the time series that corresponds to these deviations fromtrend. The method of Schreft and Singh neglects this in two important regards.First, some recessions are more severe than others. To the extent that reces-sions are temporary departures from trend, a deeper recession would naturallybe expected to be followed by higher subsequent growth in employment. TheSchreft-Singh method does not incorporate this feature. Second, their methoddoes not distinguish between movements in the trend and deviations from thetrend. If the (raw) level of employment following the trough of a recession startsto increase, how are we to know to what extent we are moving closer to trend?If the trend always increased at the same rate, this issue would be irrelevantsince it would affect all recoveries in the same fashion. However, a key featureof the post WWII labor market in the US is that trend employment growth hasfluctuated substantially over time, due both to the entry of the baby boom intothe labor market and the increased participation of women. To illustrate thisTable 1 shows the decadal growth rates in employment for the US economy forthe five decades following WWII.

Table OneEmployment Growth by Decade

1950-1960 1960-1970 1970-1980 1980-1990 1990-200020.89 26.81 23.91 17.85 17.45

The table shows that the differences are large—the decadal growth rate inemployment during the 1960’s is more than one and a half times as large as thedecadal growth rates in the two most recent decades. It follows that sortingout relative movements in trend and deviation from trend may be an importantconsideration in documenting the differential pace of employment growth duringrecoveries.Third, the method of Schreft and Singh compares the dynamics of recoveries

by examining the behavior from the turning point forward. It is not clearthat the turning point is the appropriate comparison point across cycles. Inparticular, if the downturns preceding the recoveries have been different, it isnot clear that behavior should be the same from the turning point forward. Infact, we will argue later that our model suggests that the turning point shouldnot be used as a common reference point.Having raised some issues about the statistics that Schreft and Singh report,

we now move on the describe the method that we use.

26

5.2 An Alternative Look at the Data

Our method is straightforward and is consistent with current practice in businesscycle analysis in terms of documenting properties of cyclical fluctuations. Inparticular, let Xt be a quarterly series that is seasonally adjusted for which wehave observations going from period 0 to period N . Define xt to be the log ofthe series Xt. We define the trend component of xt, denoted by xTt , by usingthe Hodrick-Prescott filter. In particular, xTt is the solution to the followingoptimization problem:

min{xTt }

N−1Xt=1

{[xt − xTt ]2 + λ[(xTt+1 − xTt )− (xTt − xTt−1)]2}

Following the literature, for quarterly data we use a value of λ = 1600.The cyclical component of xt, denoted by xCt is simply the deviation of xt

from its trend value: xCt = xt−xTt . Because the series are measured in logs, thecyclical component reflects the percent deviation of the variable from its trend.Figure 5 repeats the exercise of Schreft and Singh but uses the cyclical

component defined above as opposed to the raw data. In particular, this graphshows the percent change in the cyclical component of employment in each ofthe four quarters following the NBER turning points.8

This figure tells a similar story to the one told by Figure 3, though we notethat some details are different. In particular, whereas Figure 3 indicated thatin a typical recovery employment begins to grow as soon as the turning point isreached, Figure 5 displays that well-known feature that employment lags GDP.In particular, this Figure shows that in a typical recovery, employment begins toincrease one quarter after GDP begins to increase.9 (We note that the cyclicalcomponent of GDP defined as above has the property that the turning point forGDP following each recession coincides with the NBER turning point dates.)Next, we again ask if the recovery that began in 1970 is similar to the

two most recent recoveries. Figure 6 shows the results of carrying out theexercise analogous to that which generated Figure 4, i.e., we now consider threeindividual recoveries and compare them to the average of the other 5.We see that Figure 6 offers a very different conclusion than does Figure

4. Based on analysis of the cyclical component of the employment series, the1970 recovery also shows that even one year after the turning point employmentremains below its level at the turning point. While this picture still indicatesquantitative differences across the three recoveries, the qualitative behavior isin fact similar.

8 It is important to note that whenever one detrends the data the behavior of the cyclicalcomponent at the very beginning and end of the sample is somewhat sensitive to the initialand terminal data points. This implies that the properties of the 2001 recovery may looksomewhat different as more data becomes available.

9 See, for example the cyclical properties as report in Cooley and Prescott (1991).

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0 0.5 1 1.5 2 2.5 3 3.5 4-2

-1.5

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Quarters Since Turning Point

% C

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yclic

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others19912001

Figure 5: The 1991 and 2001 Recoveries (Detrended)

0 0.5 1 1.5 2 2.5 3 3.5 4-2

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Figure 6: Recoveries of 1970, 1991 and 2001 (Detrended)

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0 0.5 1 1.5 2 2.5 3 3.5 4-1.2

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Figure 7: Cyclical Employment, Normalized by Magnitude of Trough

These figures still suffer from the first problem we mentioned earlier—theydo not take into account the fact that the recessions vary quite substantially intheir severity, and hence we do not know how much of the variation in growthsimply reflects differences in distances from trend. There are many ways thatwe might normalize business cycles to account for the differing magnitudes. Weemploy a simple procedure here, which is to normalize by the magnitude ofthe recession as measured by the maximum percent deviation of output belowtrend. We then scale all of the employment deviations by dividing through bythe absolute value of this number. This is shown in Figure 7.Qualitatively this figure presents the same qualitative conclusions as the

earlier figure, but we note that it does impact on the quantitative differencesacross episodes.One way to summarize the properties of the above pictures are in terms of

the extent to which the turning point for employment lags the turning point forGDP. The following table shows the values for each of the post 1950 recessions.

Table 2Lag in Employment Turning Point Relative to GDP

1954 1958 1961 1970 1975 1982 1991 20011 0 1 3 1 1 6 7

This statistic confirms a property that we saw in the figures presented earlier:while a lag of 0 or 1 quarter is typical for the postwar period, there are three

29

0 1 2 3 4 5 6-2

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-0.5

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% C

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197019912001

Figure 8: Comparing the 1970, 1991 and 2001 Recoveries

recoveries in which the lag is longer, and all three of these are recoveries fromrecessions that follow long expansions. This evidence supports our earlier claimabout characterizing post war recoveries. At the same time, this table suggeststhat there is quite a significant difference between the 1970 recovery and thetwo most recent recoveries. The lags in the two most recent recoveries are infact much longer than was experienced in the 1970 recovery. In particular, ifwe extend the analysis from the four quarters following the turning point to 7quarters, then we obtain Figure 8.Figure 8 would seem to suggest that the 1970 episode is not so similar to

the two most recent ones. What we argue next, however, is that this differenceis illusory. In particular, we argue that it is driven by the choice of initialpoint, and that when this initial point is chosen in a way that we believe ismore consistent with the theory laid out earlier in the paper, the differencesdisappear.To understand the issue, consider the discussion from the previous section.

The key point there was that the time before employment begins to increaseis tied to the time required for reorganization to diminish sufficiently. The keypoint to take away from this is that the turning point is not the point at whichreorganization begins. Presumably reorganization starts to take place at somepoint during the recession preceding the recovery. This is significant becausethe duration of the recession preceding the turning point differs significantlyacross recessions. In particular, this period is either average or below average

30

for the two most recent recessions and is much above average for the 1969-1970recession.To implement this element, we need to have a method for picking out at

what point reorganization begins. One possibility would be that it begins whenthe downturn first begins. However, when a recession first begins output isstill quite high above trend and the analytic result that we proved earlier inthe paper suggested that it is the level of output that is particularly important.With this in mind we identify the point at which reorganization begins to be thefirst quarter in which the cyclical component of output lies below trend. Thefollowing table shows how many periods this lies prior to the NBER turningpoint for each of the 8 recessions. Table 3 presents the data.

Table 3Quarters Before Turning Point with GDP Below Trend1954 1958 1961 1970 1975 1982 1991 20012 2 2 4 2 4 1 2

The table indicates that the typical number of quarters that GDP is belowtrend prior to reaching its turning point is 2, but that in 1970 this value was 4,and in 1991 it was only 1.What we do next is to repeat our earlier analysis but instead of using the

turning point as the initial condition for each recession, we use the period asindicated in the above table. Once again we continue to normalize using themagnitude of the drop in GDP as our scale factor. The next graph shows theaverage of the five recessions versus each of the three more prolonged recoveries.It shows that the three recessions all stand out as different than the average

of the others. Finally, we show a comparison of the three special recessions butfor a much longer period, extending the analysis to 8 quarters. This allows usto include part of the recoveries in all three cases.To this point we have focused on employment dynamics. Employment is

simply one dimension along which labor input can vary. An important issue isthe extent to which different behavior of employment across cyclical episodesalso represent differences in labor input. Alternatively, it could be that thedominant difference across episodes is the compositional changes in labor input.More generally, one should also be concerned about measuring effective laborinput rather than simply bodies or hours. We leave a more careful analysis ofthese issues for future work, but do want to present at least one piece of evidenceto suggest that the differences in the behavior of employment that we have notedalso extend to the behavior of aggregate hours. We only have hours data from1964 on, so this analysis has only 5 cyclical episodes to compare. The nextfigure compares the three recoveries that we have focused on as compared tothe average of the other two recoveries. Period 0 in this figure refers to the firstperiod in which GDP drops below trend prior to the associated recovery.Whilethe basic pattern in this figure is qualitatively similar to the one found in ourgraphs for employment, it is also true that the differences are much smaller inthis graph than in the employment graphs. We infer from this that a more

31

0 1 2 3 4 5 6 7-1.5

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Empl

oym

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Nor

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Figure 9: Recoveries with Alternative Initial Point

0 1 2 3 4 5 6-2

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Quarters Since GDP Below Trend

Aggr

egat

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ours

(Nor

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197075-82 avg.19912001

Figure 10: Behavior of Aggregate Hours

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0 1 2 3 4 5 6-1.4

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Q t Si GDP B l T d

GD

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Figure 11: Productivity Per Employee in the 1970, 1991, and 2001 Recoveries

careful study of the behavior of labor input along the intensive and extensivemargins is warranted.Lastly, it is of interest to examine the behavior of productivity across the

cyclical episodes. Our model predicts that when organizations switch from pro-ducing to reorganizing that they experience a decrease in productivity. However,as time passes and successful reorganization occurs, we should see increases inproductivity. Having said this, we also feel that a large degree of caution needbe taken with respect to assessing the implications for productivity. We haveimplicitly assumed that aggregate fluctuations in our model are driven by shocksto the demand for the output of each organization. While this is a convenientformulation for our analysis, it could be that the increase in demand is drivenby improvements in product quality which in a more complete model would alsoshow up as productivity changes.Having offered this caveat we next turn to analyze the dynamics of produc-

tivity. Because hours data are available only since 1964, we use two differentmeasures of productivity. First we compare output per worker in order to beable to use all eight recessions, and then we use output per hour to comparethe five most recent recessions. Figure 11 shows how productivity per workerevolves in the three recoveries of interest.Note that in all cases productivity drops in the initial period but then in-

creases thereafter. While the magnitudes are somewhat different across thethree episodes, the pattern is quite similar. At a very qualitative level this

33

0 1 2 3 4 5 6-0.4

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GD

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54-58-61-75-8270-91-01

Figure 12: Comparison of Productivity per Employee Across Recoveries

seems to accord well with the implications of our model described above. Nextwe consider how productivity changes vary across the different types of recov-eries. The next figure compares the average of these three recoveries with theaverage across the other five recoveries.Both curves show the same qualitative behavior. The average of the three

recoveries following long expansions does indeed have a slightly larger drop inthe initial period and does show somewhat higher subsequent growth. Qualita-tively these patterns are consistent with what one would expect from our model,though the quantitative differences do not seem that large.Next we compare the behavior of productivity per hour for the post 1964

recoveries.This graph shows the same two features: the three recoveries associated

with recession following long expansions have a somewhat larger initial drop inproductivity and subsequently experience somewhat higher growth.

6 ConclusionWe have highlighted a simple economic mechanism that we argue may be rele-vant for understanding the different behavior of labor market aggregates acrossbusiness cycles. The model stresses two key effects. First, it argues that internalorganizational dynamics are affected by aggregate shocks. Second, it stresses

34

0 1 2 3 4 5 6-0.8

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Quarters Since GDP Below Trend

GD

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70-91-01 avg75-82 avg.

Figure 13: Comparison of Productivity Per Hour Across Recoveries

that the situations of organizations affect the manner in which the economy re-sponds to aggregate shocks. In periods of high economic activity, organizationspostpone structural changes to take advantage of current opportunities. Butonce an organization begins the process of restructuring itself, it is less likely tohire workers and more likely to release workers. These effects suggest the possi-bility that long expansions will be followed by recoveries in which employmentstarts to increase much later than output.We then assess this link by studying eight US recessions in the post 1950

period. We argue that all three recoveries from recessions that followed longexpansions exhibit the pattern of a long delay in the turning point for aggregateemployment. This finding contrasts sharply with the characterization that it isthe two most recent recoveries that are distinct.While we think this work is suggestive, we must also emphasize that it is

indeed only suggestive. A more rigorous quantitative assessment of the economicmechanism is called for, as is a more thorough analysis of the data.

References[1] Bertschek, I., and U. Kaiser, “Productivity Effects of Organizational

Change: Microeconometric Evidence,” mimeo, 2001.

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[2] Burns, A. and Mitchell, W., Measuring Business Cycles, New York, NBER,1946.

[3] Caballero, R., and E. Engel, “Explaining Investment Dynamics in US Man-ufacturing: A Generalized (S,s) Approach, Econometrica 67 (1999), 783-826.

[4] Cole, H., and L. Ohanian, “New Deal Policies and the Persistence of theGreat Depression: A General Equilibrium Analysis,” Journal of PoliticalEconomy 112 (2004), 779-816.

[5] Cooley, T. and E. Prescott, “Economic Growth and Business Cycles,” inFrontiers of Business Cycle Research, Princeton University Press, 1991,1-38.

[6] Groshen, E., and S. Potter, “Has Structural Change Contributed to a Job-less Recovery?,” Federal Reserve Bank of New York Current Issues in Eco-nomics and Finance, Volume 9, no. 8, 2003.

[7] Hall, R., “Labor Demand, Supply and Employment Volatility,” NBERMacroeconomics Annual, edited by Olivier Blanchard and Stanley Fischer,MIT Press, 1991, 17-61.

[8] Hopenhayn, H., “Entry, Exit and Firm Dynamics in the Long Run,” Econo-metrica 60 (1992), 1127-1150.

[9] Hopenhayn, H., and R. Rogerson, “Job Turnover and Policy Evaluation: AGerneral Equilibrium Analysis,”, Journal of Political Economy 101 (1993),915-938.

[10] Koenders, K., “Long Expansions and Slow Recoveries: A Closer Look atEmployment Fluctuations,” mimeo, ASU, 2004.

[11] Krusell, P., and T. Smith, “Income andWealth Heterogeneity in the Macro-economy,” Journal of Political Economy 106 (1998), 867-896.

[12] Lilien, D., “Sectoral Shifts and Cyclical Unemployment,” Journal of Polit-ical Economy 90 (1982), 777-793.

[13] Lucas, R., “Understanding Business Cycles,” Carnegie-Rochester Series onPublic Policy 5 (1977), 7-29.

[14] Lucas, R. “On the Size Distribution of Business Firms,” Bell Journal ofEconomics 9 (1978), 508-523.

[15] Schreft, S., and A. Singh, “A Closer Look at Jobless Recoveries,” FederalReserve Bank of Kansas City Economic Review, Second Quarter, 2003,45-73.

[16] Schweitzer, M., “Another Jobless Recovery?,” Federal Reserve Bank ofCleveland Economic Commentary, March 1, 2003.

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[17] Thomas, J., “Is Lumpy Investment Relevant for the Business Cycle?,” Jour-nal of Political Economy 110 (2002), 508-534.

[18] Veracierto, M., “Plant Level Irreversible Investment and the Business Cy-cle,”, American Economic Review 92 (2002), 181-197.

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